Pneumatic artificial muscles (PAMs) are an important type of bionic actuators for high power-to-weight ratio and good flexibility. However, nonlinearities always exist in systems driven by PAMs, which should be dealt with to obtain good performances during position control. In this paper, a nonlinear state error feedback controller (NSEFC) is presented to obtain good position accuracy for a two-joint manipulator system driven by PAMs. The two-joint manipulator system has nonlinearities, which come from friction, hysteresis, uncertainties of model, loss of piping pressure, coupling between two joints, and so on. A nonlinear extended state observer (ESO) is designed to estimate the nonlinearities in the two-joint manipulator system. Both the effectiveness of the nonlinear ESO and stability of the two-joint manipulator system are given by Lyapunov approaches. Experimental results are obtained to show that the position accuracy of the two-joint manipulator system is improved based on the proposed method in this paper.